Difference between revisions of "The Golden Ratio or phi"
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Nobody likes the <math>\approx</math> symbol. They prefer the <math>=</math> symbol or inequalities. However, this symbol is needed when working with Fibonacci numbers. For example the approximation: <math>F_n-1 + \frac{1+\sqrt{5}}{2} \approx F_n</math>, where F stands for Fibonacci number. | Nobody likes the <math>\approx</math> symbol. They prefer the <math>=</math> symbol or inequalities. However, this symbol is needed when working with Fibonacci numbers. For example the approximation: <math>F_n-1 + \frac{1+\sqrt{5}}{2} \approx F_n</math>, where F stands for Fibonacci number. | ||
| − | But there is an exact formula for Fibonacci numbers that have no <math>\approx</math> symbol. | + | But there is an exact formula for Fibonacci numbers that have no <math>\approx</math> symbol. |
| + | [[Binet’s Formula]]: | ||
<math>F_n=\dfrac{1}{\sqrt{5}}\left( \left( \dfrac{1+\sqrt{5}}{2}\right)^n - \left( \dfrac{1-\sqrt{5}}{2}\right)^n \right)</math> | <math>F_n=\dfrac{1}{\sqrt{5}}\left( \left( \dfrac{1+\sqrt{5}}{2}\right)^n - \left( \dfrac{1-\sqrt{5}}{2}\right)^n \right)</math> | ||
Revision as of 12:21, 1 January 2024
Nobody likes the 
symbol. They prefer the 
symbol or inequalities. However, this symbol is needed when working with Fibonacci numbers. For example the approximation: 
, where F stands for Fibonacci number.
But there is an exact formula for Fibonacci numbers that have no symbol.
Binet’s Formula:
